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  4. A thin metal square plate has length l. When it is heated from 0° C to 100° C, its length increases by 1 %. What is the percentage increase in the area of the plate ?

Q. A thin metal square plate has length $l$. When it is heated from $0^{\circ} C$ to $100^{\circ} C$, its length increases by $1 \%$. What is the percentage increase in the area of the plate ?

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Solution:

Let original area of square plate is $A=l^{2}$
New length, $l=l+\frac{l}{100}=\frac{101 l}{100}$
New Area, $A^{\prime}=\left(l^{\prime}\right)^{2}=1.0201 l^{2}$
Percentage increase in area
$=\frac{A^{\prime}-A}{A} \times 100$
$=\frac{1.0201-1}{1} \times 100$
$=2.01 \%$

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